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We consider asymptotics behavior of Poissonized Plancharel measures as thepoissonization parameter $N$ goes to infinity. Recently Moll proved aconvergent series expansion for statistics of a measure $\mu_\lambda$ which isthe Kerov-Markov-Krein transform of the signed measure on corners a Jack-randompartition $\lambda$. The measure $\mu_\lambda$ is of interest because itbehaves in some ways like the empirical measure on eigenvalues of a GUE-randommatrix. We prove for the Poissonized Plancharel case that the large $N$ seriesfor moments of $\mu_\lambda$ have a recursive structure as rational expressionsin the generating function for Catalan numbers. We discuss the analogy betweenour result and the fine structure of moments of the GUE.

Fine structure of moments of the KMK transform of the Poissonized Plancharel measure